Unfortunately, generally speaking opening up a permanent magnet chuck like that either ruins it or at least degrades the holding power. It has something to do with the laminations acting like "keepers"- like the extra bar of metal they used to leave between the ends of old horseshoe magnets.
Pry the keepers out of place and it damages the magnets- I don't fully understand the mechanics of it (f**kin' magnets, how do they work?

) but it's something like the magnets are powerful enough they essentially aren't structurally strong enough to resist their own power. If that makes any sense.
Pry the keepers out of place and the magnets crack or try to destroy their own poles.
Now, that said, if you can open the base and find the lever mechanism is stuck (rust from flood coolant, dried oil, general gunk, etc.) you may be able to clean and lube it without dismantling the laminations.
However, even if it was fully functioning, as noted above, that's a fairly specialized tool, basically used only with a surface grinder. Even at full power, it won't have enough holding power for milling or drilling (besides not having any through clearance for drilling.)
Doc.